High dimensional expanders and coset geometries

Understand

High dimensional expanders is a vibrant emerging field of study.

• Nevertheless, the only known construction of bounded degree high dimensional expanders is based on Ramanujan complexes, whereas one dimensional bounded degree expanders are abundant.
• In this work, we construct new families of bounded degree high dimensional expanders obeying the local spectral expansion property.
• This property has a number of important consequences, including geometric overlapping, fast mixing of high dimensional random walks, agreement testing and agreement expansion.